Solve 3sqrt{32}-5sqrt{8}

$$3 \sqrt { 32 } - 5 \sqrt { 8 }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$3\times 4\sqrt{2}-5\sqrt{8}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{2}-5\sqrt{8}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$12\sqrt{2}-5\times 2\sqrt{2}$$

Multiply -5 and 2 to get -10.

$$12\sqrt{2}-10\sqrt{2}$$

Combine 12\sqrt{2} and -10\sqrt{2} to get 2\sqrt{2}.

$$2\sqrt{2}$$